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Optimization of organic Rankine cycle (ORC)
based waste heat recovery (WHR) system using a
novel target-temperature-line approach
Md. Zahurul Haq
Professor, Department of Mechanical Engineering,
Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh
Email: [email protected], [email protected]
www: http://zahurul.buet.ac.bd/
ABSTRACT
Organic Rankine cycle (ORC) based waste heat recovery (WHR) systems are simple, flexible, economical
and environment-friendly. Many working fluids and cycle configurations are available for WHR systems, and the
diversity of working-fluid properties complicates the synergistic integration of the efficient heat exchange in the
evaporator and net output work. Unique guidelines to select proper working-fluid, cycle configuration and optimum
operating parameters are not readily available. In the present study, a simple target-temperature-line approach is
introduced to get the optimum operating parameters for the sub-critical ORC system. The target-line is the locus of
temperatures satisfying the pinch-point-temperature-difference along the length of the heat-exchanger. Employing
the approach, study is carried out with 38 pre-selected working fluids to get the optimum operating parameters
and suitable fluid for heat source temperatures ranging from 100oC to 300oC. Results obtained are analysed to get
cross-correlations between key operating and performance parameters using heat-map diagram. At the optimum
condition, optimal working fluid’s critical temperature and pressure, evaporator saturation temperature, effective-
nesses of the heat exchange in the evaporator, cycle and overall WHR system exhibit strong linear correlations with
the heat source temperature.
Keywords: Organic Rankine cycle (ORC), Waste heat recovery (WHR), Energy efficiency, Pinch point, Ther-
modynamic optimization.
JERT-20-1857 1 Haq
Nomenclature
D heat exchanger duty (J)
h, H enthalpy (J/kg, J)
I irreversibility (J)
P pressure (Pa)
r (Pearson’s) correlation coefficient
T temperature (oC)
W work (J)
Greek Letters
ε (second-law) effectiveness
η first-law efficiency
Ψ, ψ flow-exergy (J, J/kg)
Superscripts and Subscripts
. (e.g. m, W ) rate of (e.g. mass flow, work)
0 environmental state
01–06 thermodynamic state points
c cold fluid stream
cr critical-point state
cy cycle
evap evaporator
h hot fluid stream
ht heat transfer
in inlet
net net
o overall
out outlet
p pump
pp pinch point
sat saturated condition
t turbine
wf working fluid
Acronyms
ORC organic Rankine cycle
WHR waste heat recovery
JERT-20-1857 2 Haq
1 Introduction
With the increasing uncertainty in the supply and price of fuels, and the global warming challenges because of green-
house gas (GHG) emissions, efficient energy conversion is vital to simultaneously address energy security and environmental
issues. During conversion to useful work, around half of the primary energy is lost as ‘waste heat’ and 40% of the lost heat
is in the temperature ranging from 80oC to 300oC [1]. Hence, ‘waste heat’ is defined as ‘waste heat as a resource is exergy
that unavoidably leaves a process or is lost within it independent of the technological choices made within the process’ [2].
Effective utilization of waste heat boosts overall system performance with simultaneous reduction in primary energy con-
sumption and carbon footprint [3]. Among the technologies to convert the medium-to-low grade thermal energy into power,
waste heat recovery (WHR) systems based on organic Rankine cycle (ORC) offer the advantages of flexibility, efficiency,
simplicity, safety and stability [4]. Turbines built for ORC systems typically require single stage-expander, resulting in a
simple and economical system in terms of capital costs and maintenance [5].
Recently, research and applications of ORC based WHR systems are expanding globally. These are implemented to
economically utilize waste heat from engines (e.g. automotive- [6], Diesel- [7] and gas- [8] engines), industrial processes
(e.g. cement [9], steel [10], smelting furnace gases [11], boiler flue gas [12], etc.) and renewable energy sources like
geothermal [13, 14], solar thermal [15], biomass [16], etc. The availability of various working fluids [5, 17], optimized
components [18,19] and design alternatives for cycle/configuration [13,20] enable the ORC systems to economically operate
in a wide range of heat source temperatures and capacities.
In the WHR system, hot source fluid forms an external coupling with the evaporator of the ORC. The variation in the
heat capacity rates of the heat source fluid is small and therefore exhibit essentially linear heat-release-curve. However,
thermophysical properties of the working fluids differ remarkably in preheating, evaporation and super-heating, and typical
heat absorption curve is a poly-line in the T-S diagram [4]. So, local heat capacity rates of the heat exchanging fluids are not
well-matched in the evaporator and the unavoidable temperature difference leads to the major contribution to overall exergy
destruction [21].
For a heat source, several thermophysical properties are to be weighted to select proper working fluid: molecular-
structure and complexity, fluid’s critical properties, normal boiling point and evaporation pressure, latent heat of evaporation,
liquid and two-phase heat capacities and the slope of the fluid vapour saturation line in T-S diagram, etc. [20]. Addressing
all these parameters is tedious, and fluid’s critical temperature is the commonly used parameter for the selection of potential
working fluids [20]. The slope of the expansion process of the working fluid in a T-S diagram is also important: the slope
can be positive, negative or vertical and the fluids are accordingly termed as ‘dry’, ‘wet’ and ‘isentropic’, respectively [22].
Isentropic and dry fluids are widely used in the ORC systems as wet fluids need to be superheated to minimize turbine blade
‘pitting’ caused by fluid droplets during expansion. However, if the fluid is too dry, the expanded fluid leaves with substantial
superheat causing energy loss [5]. Recently, some fluids are fruitfully classified as ‘super dry’ [23].
To recover waste heat, several cycle configuration/options are available [1, 20]. A trans-critical cycle can increase the
efficiency; however, with lower heat absorption capacity and the adaptability to different heat sources [4]. Dual-pressure
evaporation may significantly increase the heat absorption capacity with improved adaptability to heat sources, while the
temperature difference between the fluids remains large for high-temperature heat sources [4]. Dual-loop systems achieve
the maximum power output; however, these are large, complex and often economically unfavourable, particularly for the
automotive applications [6]. Updated version of a single-loop system can overcome some of the limitations [6]. At a source
temperature, optimized single-loop ORC system with a pure working fluid can provide important guidance to design mixture
JERT-20-1857 3 Haq
working fluid for proper thermal matching for high heat exchange efficiency [24].
For maximum heat recovery, ‘pinch point’ analysis is vital [25]. Costs of the WHR systems decrease with an increase
in pinch point temperature difference, ∆Tpp, while the exergy destruction in the evaporator is increased [26]. With every 1oC
decrease in evaporator ∆Tpp, ORC systems produce 1.7 - 2.6% more net work output [27]. Hence, proper selection of ∆Tpp
is vital to optimize efficiency and capital investment, as heat-exchangers (evaporator and condenser) account for the largest
portion of the required investment [23]. The optimal value of ∆Tpp are reported in the range of 5-12oC [21], and 7-10oC [28];
and, ∆Tpp = 10oC is widely used [29]. Several alternative approaches are employed to implement pinch in the heat-exchanger
design: pinch and exergy are integrated into heat exchanger network (HEN) [30, 31]; suitable algorithm is applied to predict
pinch point locations in the heat-exchanger and then optimization is sought [32]; by defining parameters to address preheating
and vaporizing pinch points followed by the optimization of the operating parameters [33], using a framework enabling the
simultaneous optimization of the processes [34]. Recently, Rad et al. [29] proposed some simultaneous optimization of the
working fluid and the operating parameters; however, evinced the non-availability of a unique procedure to achieve maximum
utilization of the waste heat.
Experimental works form a small fraction of the published literature in the ORC-technology and experimentations are
often carried out for various heat source fluids (e.g. hot exhaust gases, water, oil etc.) at various temperatures and are
subjected to various environmental states. Most of the experimental ORC-systems are constructed with basic ORC configu-
rations predominantly for low-medium temperature heat sources because of the huge potential of the industrial applications,
and R245fa is found to be the most popular working fluid [35]. Feng et al. [36] reported the experimental comparison of
the performance of the basic and regenerative ORC systems using R245fa as the working fluid, and observed the lower tem-
perature utilization of the regenerative ORC systems than the basic ORC systems as the addition of the regenerator leads to
the heating of the working fluid entering the evaporator resulting in reduced heat absorbency. Moreover, the addition of the
recuperator/regenerator increases in the capital cost and the space requirement to put some limitations for some applications,
especially for low-medium temperature heat sources. Recently, based on the survey of more than 200 experimental ORC
systems, the maximum output of the systems are found around 7% lower than the target power or the nominal power of the
expander requiring to oversize the systems by at least 7% further [35].
In the present study, a simple approach using a target-temperature-line is proposed and demonstrated to select optimal
working fluid and optimum operating parameters for the sub-critical ORC system to maximize the waste heat utilization.
The proposed method decouples the heat exchange process from the power cycle, and provides a range of feasible operating
parameters satisfying the design constraints for the heat exchangers. The approach is simple to implement and applicable
for pure working fluids and fluid-mixtures. The feasible operating parameters are then used for the detailed optimization
of the power cycle. In the present paper, study is reported for heat sources at 9 different temperatures ranging from 100 to
300oC, and key operating and performance parameters are obtained for the sub-critical ORC based WHR systems. At the
optimum condition(s) with optimal working fluid(s), optimal fluid’s critical temperature and pressure, the cycle’s evaporator
saturation temperature and some key performance parameters are found to exhibit strong linear correlations with the heat
source temperatures.
JERT-20-1857 4 Haq
2 Methodology
2.1 Thermodynamic Model
Waste heat recovery (WHR) system, considered in the present study, is based on the organic Rankine cycle (ORC)
which is composed of four key components as shown in Fig. 1, and the thermodynamic state-points are designated by
two-digit numbers. Hence, heat source fluid forms an external coupling with the evaporator of the ORC system and three
physical/virtual regions could be identified in the evaporator: ‘H-01’ is the pre-heater/economiser, evaporation occurs at
‘H-02’ and ‘H-03’ is the super-heater; and superheating of the working fluid may not occur and evaporation then continues
in the last two regions. Working fluid vapour, generated in the evaporator, is expanded in the turbine (expander) to produce
useful work. Vapour leaving the turbine is then condensed to saturated state and pumped back to the evaporator for the cycle
completion. In the present study, steady-state-steady-flow (SSSF) operation and negligible pressure drops in the evaporator,
condenser and the piping system are assumed. In general, variation in the heat capacity rates of heat source fluid (e.g. exhaust
gases, waste hot water etc.) is small and dry-air is assumed as the heat source fluid in the present study to demonstrate the
proposed methodology which can be applied even if the heat exchanging fluids exhibit variable heat capacity or even phase
change(s). When exhaust gases are used as the heat source, chimney draught requirement and the dew-point temperature
of the gas impose some limitations of the final outlet temperature. Rad et al. [29], used 60oC as the final exit temperature
assuming the absence of sulphur in the exhaust gases. In the present study, evaporator outlet temperature is assumed to be
60oC to assess the maximum feasible heat recovery from the waste heat source. Some base-operating-parameters of the
present study are reported in Table 1.
01
02 03
04
0506
WpPump
WtTurbine
cooling water
Condenser
H-01 H-02 H-03
3a 3b
Evaporator
Hot source fluidmh
mwf
Fig. 1: Schematic block diagram of the system.
If energy balance is performed on each of the system components, the ‘SSSF energy equation’, neglecting the change in
potential and kinetic energy, can be written, in general, as [38]:
Q = W +out
∑i
mihi −in
∑i
mihi (1)
where Q is the heat transfer rate into the component, mi is the working fluid’s mass flow rate at section ‘i’, hi is the enthalpy
at section ‘i’ and W is the work rate by the component. Similarly, the ‘SSSF exergy equation’ can be expressed as [38]:
ΦQ = W +out
∑i
miψi −in
∑i
miψi + I (2)
JERT-20-1857 5 Haq
Table 1: Base-operating-parameters of the WHR system.
Parameter Symbol Value
Hot Source
Fluid [37] Dry air
Mass flow rate mh 1.0 kg/s
Inlet temperature Th,in [100-300]oC
Outlet temperature [29] Th,out 60oC
ORC system
Condenser pressure [29] Pcond sat. at 30oC
Evaporator saturated temperature Tevap,sat ≤ 0.95Tcr
Fluid quality in/out turbine [29] X03, X04 ≥ 0.90
Pump isentropic efficiency [29] ηp 0.70
Turbine isentropic efficiency [29] ηt 0.85
Pinch-point temperature difference [29] ∆Tpp 10oC
Environmental State
Temperature T0 25oC
Pressure P0 0.1 MPa
where ΦQ ≡ ∑Qi
(
1− T0Ti
)
is the exergy transfer associated with heat transfer, I accounts for exergy destruction because of
internal irreversibility in the component and ψi is the flow-exergy at section ‘i’. Hence, flow-exergy is defined as:
ψ ≡ (h−h0)−T0(s− s0) (3)
where, kinetic and potential energies are omitted, and the subscript ‘0’ represents the properties of the fluid at (restricted)
equilibrium with the environment [39] and T0 is expressed in absolute scale.
In the evaporator, heat source fluid enters at Th,in and leaves at Th,out, and no work is produced. Considering negligible
heat exchange with the environment, simplified energy and exergy balance equations (Eqs. 1 and 2), respectively, are:
mwf(h03 −h02) = mh(h05 −h06) (4)
mh(ψ05 −ψ06) = mwf(ψ03 −ψ02)+ Ievap (5)
where, mh and mwf are the mass flow rates of the source and working fluids, respectively.
In the evaporator, supplied exergy, ∆Ψh = mh(ψh,in − ψh,out) = mh(ψ05 − ψ06), is not completely transferred to the
working fluid and significant exergy destruction occurs. Figure 2 shows two isobaric heat exchange processes on a typical
T − S diagram, following [39], and the areas under the lines Th,in − Th,out and Tc,in − Tc,out are equal. Since I = T0 ∑∆S, the
shaded area represents the irreversibility, Ievap, because of heat exchange process. As the process profiles on T − S diagram
approaches each other, irreversibility is reduced. In the condenser, temperature difference between the heat exchanging fluids
is small and generated irreversibility is often neglected [39].
Processes in the pump and the turbine are essentially adiabatic in nature. So, using Eq. 1, the pump and turbine works
can be written, respectively, as:
Wp = −mwf(h02 −h01) (6)
Wt = mwf(h03 −h04) (7)
Using Eq. 2, irreversibility in the pump and in the turbine can be written, respectively, as:
Ip = −Wp − mwf(ψ02 −ψ01) (8)
It = −Wt − mwf(ψ04 −ψ03) (9)
JERT-20-1857 6 Haq
Th,in
T0
S
T
T03
Tc,in
Tc,out
T02
T06
T05
Th,out
I = T0∆S
Fig. 2: Irreversibility because of heat-exchange process.
2.2 Performance Indicators
Efficiency is widely used to indicate the performance of a system. However, efficiency can have different meanings and,
unaccompanied by a formal definition or taken out of context, can lead to serious misconceptions [40]. Efficiencies based on
the first-law of thermodynamics fall into two general categories [39]:
1. ‘Thermal efficiency’, which compares the desired energy output to the required energy input [38, 39], that is,
ηth ≡ Energy out in product
Energy in=
Energy out in product
Energy out in product + Energy loss(10)
where, the term product may refer to shaft work or generated electricity, some desired combination of heat and work
etc., and losses include such things as waste heat or stack gases vented to surroundings without use [38].
2. Equipment first-law efficiency, widely known as ‘first-law efficiency’ or ‘isentropic efficiency’, and it compares the actual
energy change to some theoretical energy change under specified condition. Many work producing/absorbing devices
operate approximately adiabatic, and the comparison is often made with isentropic condition with the same initial state
and the final pressure [39]. Accordingly, isentropic efficiency of the turbine and the pump can be written, respectively,
as:
ηt ≡ Wt
Wt,s
=h03 −h04
h03 −hs,04(11)
ηp ≡ Wp,s
Wp
=hs,02 −h01
h02 −h01(12)
where hs,04 is the fluid enthalpy for isentropic expansion in the turbine and hs,02 is the fluid enthalpy for isentropic
compression in the pump.
Efficiency parameters based on first-law of thermodynamics make no distinction between work, heat and other forms of
energy. To address the potential of heat to produce useful work, performance based on exergy concept is known as a ‘second-
law’ or ‘exergetic efficiency’, ηII, or as ‘second-law effectiveness’, or simply as an ’effectiveness’, ε. Typical definition of
second-law effectiveness, ε is [38, 40]:
ε ≡ Exergy out in product
Exergy in(13)
Hence, the effectiveness of the WHR system is the net work output divided by the exergy input associated with the heat
source; that is,
εo ≡ Wnet
Ψh,in
=Wnet
mhψh,in
=Wnet
mhψ05
(14)
JERT-20-1857 7 Haq
Table 2: Pre-selected working fluids.
w. fluid Tcr Pcr type w. fluid Tcr Pcr type w. fluid Tcr Pcr type
[oC] [MPa] [23] [oC] [MPa] [23] [oC] [MPa] [23]
R1216 85.75 3.1495 Isen. R245fa 153.86 3.651 Dry heptane 267.05 2.7357 S. Dry
R1234yf 94.7 3.3822 Isen. R1233zd(E) 166.45 3.6237 Isen. isooctane 270.85 2.572 S. Dry
R227ea 101.75 2.925 Dry R245ca 174.42 3.9407 Dry cyclohexane 280.45 4.0805 Dry
R1234ze(E) 109.36 3.6349 Isen. R123 183.68 3.6618 Isen. benzene 288.87 4.9073 S. Dry
perfluorobutane 113.18 2.3224 Dry R365mfc 186.85 3.266 Dry octane 295.59 2.4836 S. Dry
RC318 115.23 2.7775 Dry isopentane 187.2 3.378 S. Dry D4 313.35 1.3472 S. Dry
R124 122.28 3.6243 Isen. R141b 204.35 4.212 Isen. toluene 318.6 4.1263 S. Dry
R236fa 124.92 3.2 Dry R113 214.06 3.3922 Dry nonane 321.4 2.281 S. Dry
isobutane 134.66 3.629 Dry isohexane 224.55 3.04 S. Dry p-Xylene 343.02 3.5315 S. Dry
R236ea 139.29 3.42 Dry pentane 232.85 3.1845 S. Dry m-Xylene 343.74 3.5346 S. Dry
isobutene 144.94 4.0098 Isen. hexane 234.67 3.0441 S. Dry ethylbenzene 343.97 3.6224 S. Dry
butene 146.14 4.0051 Dry cyclopentane 238.57 4.5828 Dry decane 344.55 2.103 S. Dry
butane 151.98 3.796 Dry MM 245.55 1.9311 S. Dry
Heat-exchange effectiveness in the evaporator, εht, is the exergy gain of the working fluid divided by the decrease of the
exergy of the heat source fluid, that is,
εht =∆Ψc
−∆Ψh
=mwf(ψ03 −ψ02)
mh(ψ05 −ψ06)(15)
and, effectiveness of the ORC, εcy, can be expressed as:
εcy =Wnet
Ψcy,in
=Wnet
mwf(ψ03 −ψ02)(16)
So, several performance indicators are available for the WHR systems; however, waste heat recovery and output power
are not generally maximized at peak thermal efficiency [1]. Recently, exergy is opined as ‘the only rational basis’ to assign
monetary values and environmental impacts to energy conversion processes and associated thermodynamic inefficiencies
within it [41]. Exergy losses indicate the scope of thermodynamic improvement, and therefore exergy based performance
indicator, embedded in the concept of effectiveness, is used in the present study to identify the optimum performance of the
system.
2.3 Preliminary Selection of Working Fluids
Critical temperature and type of the working fluid are widely used to pre-select the fluid. For a given heat source
temperature, Th,in, J. Hærvig et al. [37] reported that the optimal fluid has a critical temperature within 30oC to 50oC below
Th,in; however, Rad et al. [29] considered all the fluids with critical temperatures in the range of ± 40oC of Th,in. In the
present study, fluids having critical temperatures within ± 50oC of Th,in are considered in the fluid pre-selection and ‘wet’
fluids are excluded. Hence, total 38 fluids are considered and are listed in Table 2, and temperature-wise list is reported in
Table 3.
2.4 Estimation of Thermophysical Properties
Thermophysical properties of the working fluids are estimated using REFPROP ver. 10 [42], which is developed by the
National Institute of Standards and Technology (NIST) for the calculations of thermodynamic and transport properties of
important pure and mixtures fluids. Present thermodynamic model is implemented in Python programming language, and
COOLPROP [43] utilities are used to access the REFPROP library and to validate some property data. To validate, data and
JERT-20-1857 8 Haq
Table 3: Temperature-wise pre-selected working fluids.
Heat source gas temperature, Th,in
100oC 125oC 150oC 175oC 200oC 225oC 250oC 275oC 300oC
R1216 R12161 R227ea isobutane butane R123 R141b pentane heptane
R1234yf R1234yf R1234ze(E) R236ea R245fa R365mfc R113 hexane isooctane
R227ea R227ea perfluorobutane isobutene R1233zd(E) isopentane isohexane cyclopentane cyclohexane
R1234ze(E) R1234ze(E) RC318 butene R245ca R141b pentane MM benzene
perfluorobutane perfluorobutane R124 butane R123 R113 hexane heptane octane
RC318 RC318 R236fa R245fa R365mfc isohexane cyclopentane isooctane D4
R124 R124 isobutane R1233zd(E) isopentane pentane MM cyclohexane toluene
R236fa R236fa R236ea R245ca R141b hexane heptane benzene nonane
isobutane isobutane isobutene R123 R113 cyclopentane isooctane octane p-Xylene
R236ea R236ea butene R365mfc isohexane MM cyclohexane D4 m-Xylene
isobutene isobutene butane isopentane pentane heptane benzene toluene ethylbenzene
butene butene R245fa R141b hexane isooctane octane nonane decane
butane R1233zd(E) R113 cyclopentane
R245fa R245ca isohexane MM
R1233zd(E) R123
R245ca R365mfc
isopentane
1Non-feasible solution, no solution is found to satisfy all the imposed conditions.
Table 4: Validation using energy and exergy accounting data of a steam power plant.
Parameter(s) present study Data [39]
Qboiler, Qcond [kJ/kg] 3315.9, -2097.9 3314.4, -2097.5
Wt, Wp [kJ/kg] 1238.1, -20.06 1237.0, -20.1
ψboiler, ψcond [kJ/kg] 1510.0, -75.68 1509.5, -75.9
ψt, ψp [kJ/kg] -1449.0, 14.28 -1447.9, 14.3
It, Ip [kJ/kg] 210.6, 5.78 210.9, 5.8
results reported in the literature are checked (e.g. [39], [43]), and one particular case is presented in Table 4 where energy
and exergy accounting of a Rankine cycle is compared. Good agreements are observed between the obtained results and
reported in [39].
2.5 Estimation of Optimum Operating Parameters using the Target-temperature line
In the present study, a ‘target-temperature line’ approach is introduced to estimate the optimum operating parameters.
Neglecting the heat losses to the environment, heat delivered to working fluid is known as ‘Duty’ of the heat exchanger [44],
and its value can be estimated using:
D = −∆Hh = mh(h05 −h06) (17)
To construct the ‘target-temperature line’, D is equally divided into 1000 parts along the length of the heat exchanger,
and at an intermediate duty D j, the corresponding heat source fluid temperature, Th, j, is estimated from the calculated value
of hh, j using the heat balance equation:
D j =j
1000D = mh(hh, j −h06) (18)
here, h06 is the enthalpy of the heat source fluid leaving the evaporator. The target temperature, Tr, j, is estimated using:
Tr, j = Th, j −∆Tpp (19)
JERT-20-1857 9 Haq
where ∆Tpp is pinch point temperatures difference. The target-temperature line construction is illustrated in Fig. 3. At a given
D j, the working fluid is assumed saturated at Tr, j; so, Tevap,sat, j = Tr, j and Pevap, j is the corresponding saturation pressure.
Hence, D j is consumed to preheat the working fluid to the saturated state and the energy balance is used to calculate mwf, j,
that is,
mwf, j =D j
(hj −h02)(20)
here, h02 is the enthalpy of the working fluid entering into the evaporator and h j is the enthalpy of the saturated fluid at Tr, j.
Th,in
Tc,in
Duty, D
Tem
perature
jj = 0 j = 1000
Th,outTar
getline
Enthalpy
Hh,out
Hh,in
D1000
Dj = j1000
D
mhhh,j = Hh,out + Dj : ⇒ Th,j
Tr,j = Th,j − ∆Tpp
Fig. 3: Graphical demonstration of the target-temperature line construction.
Once the values of Pevap, j and mwf, j are known, possible state of the fluid leaving the evaporator, state 03, may be
estimated using the overall energy balance for the evaporator; that is,
h03, j = h02 +D
mwf, j
(21)
However, T03, j may hypothetically exceed the target-temperature to satisfy the energy balance equation (Eq. 4), and
constitutes the violation of design constraint (∆Tpp) and the second-law of thermodynamics. If T03, j > (Th,in − ∆Tpp), the
solution is non-feasible, and if the fluid is leaving the evaporator in two-phase state with X03 < 0.9, the solution is also
ignored. If Tevap,sat, j > 0.95Tcr, the solution is also discarded (Table 1). The procedure is also illustrated in Fig. 4.
Th,in
Tc,in
Duty, D
Tem
perature
jj = 0 j = 1000
Pevap,j = Psat(Tr,j)
mwf,j =Dj
hj−hc,in
Th,out
Tc,out
∆Tpp
Target
line
√
√
×
Fig. 4: Illustration of the estimation of the operating parameters.
JERT-20-1857 10 Haq
By considering the pinch point to occur along the length of the heat exchanger, a range of feasible operating parameters
(Pevap, Tevap,sat, T03 and mwf) are estimated. Detailed thermodynamic analysis of the cycle is then carried out for all these
cases. However, if X04 < 0.9, the solution is also discarded, and this scenario will not prevail for dry/isentropic fluids.
Based on all the feasible solutions, overall exergy efficiency, εo, is estimated and the condition that yields the maximum
value of εo is the optimum operating condition of the working fluid for Th,in. At a given Th,in, analysis is done for several
pre-selected working fluids and the working fluid providing the maximum εo is selected as the optimum working fluid and
the corresponding operating parameters are chosen for the source temperature.
3 Results and Discussions
Shown in Fig. 5 is an example of the target-temperature line method applied for Th,in = 100oC using R1216 as the working
fluid. Using Eq. 17, we get, D = 40.6 kW, and D is equally divided into 1000 parts along the length of the heat-exchanger
(evaporator) and calculations are done for all the cases. In Fig. 5, only 5 representative cases are presented and some key
results are also noted. Hence, cases 2© and 3© are feasible solutions, and in-between these there are 179 intermediate feasible
solutions. Three other cases of Fig. 5 are non-feasible because of the following reasons:
Case 1©: T03 > (Th,in −∆Tpp),
Case 4©: Tevap,sat > 0.95Tcr,
Case 5©: Tevap,sat > 0.95Tcr, X03 < 0.90.
30
40
50
60
70
80
90
100
110
120
0.0 0.2 0.4 0.6 0.8 1.0
Tem
pera
ture
(oC
)
Dj/D
R1216, Th,in = 100oC
1©2©3©4©5©
Target temperatureHot source temperature
case Dj/D mwf (kg/s) Pevap (MPa) Tevap,sat (oC) T03 (oC) X03 X04 ǫo (%)
1○ 0.197 0.220 1.72 57.9 119.8 >>1.0 >>1.0 27.532○ 0.263 0.266 1.83 60.5 89.9 >>1.0 1.33 30.593○ 0.444 0.355 2.14 67.8 67.8 0.914 0.993 34.994○ 0.451 0.357 2.18 68.7 68.7 0.901 0.985 35.035○ 0.558 0.390 2.40 72.3 72.3 0.7367 0.900 35.89
Fig. 5: Estimation of the operating parameters for Th,in = 100oC using R1216.
The estimated values of mwf and fluid temperatures in the evaporator sections (Fig. 1) versus Pevap are plotted in Fig. 6.
Hence, lines are drawn to present all the results and symbols are used to show the feasible solutions. It is seen that the feasible
solutions are within narrow ranges of evaporator saturation pressure, temperature and mass flow rate. It is also seen that, at
low values of mwf and Pevap, fluid vapour leaves the turbine superheated and the super-heating diminishes with increase in
Pevap.
Shown in Fig. 7(a) is the energy-flow diagram, for the optimal operating condition for Th,in = 100oC using R1216.
Optimum performance is achieved at case 3© of Fig. 5. Hence, only 4.4% of the waste heat is converted to turbine work, the
JERT-20-1857 11 Haq
25
50
75
100
125
150
175
200
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Tem
pera
ture
(oC
)
Mass
flow
rate
,m
wf
(kg/s
)
Evaporator pressure, Pevap (MPa)
R1216, Th,in = 100oC
mwf
T3a, T3b
T03
Fig. 6: Variation of mwf and temperatures of the working fluid in the evaporator.
pump work is equivalent to 0.7% of heat yielding only 3.8% of the heat to the net output work, and also it seen that pump
work is not negligible as compared to turbine work which is common in water-based Rankine cycle. So, overall thermal
efficiency is only 3.8%, and 46.6% of the waste heat is exhausted with the hot gases leaving the evaporator at 60oC, and
49.6% heat is rejected to the condenser. However, exergy-flow diagram, shown in Fig. 7(b), depicts significantly different
scenario: only 2.8% of the exergy is lost to the condenser, 23.5% is lost with the hot exhaust gases and 35.0% of exergy is
converted to net output work. Hence, overall effectiveness of the system is 35.0%. Figure 7(b) shows some details of the
exergy consumption: 25.0% is lost due to irreversibility in the evaporator, 11.9% is lost because of turbine irreversibility and
1.8% is lost in the pump. Hence, the evaporator is the component where significant exergy destruction occurs and warrant
proper thermal matching between the heat exchanging fluids.
evaporatorQh, in100.0%
Qh, out46.6%
turbine
Wt4.4%
Wnet3.8%
Wp0.7%
condenser Qcond49.6%
pump
(a) Energy flow.
evaporatorΨh, in
100.0%
Ψh, out23.5% Iht
25.0%
turbine
Wt41.1%
It11.9%
Wnet35.0%
Wp6.2%
condenserΨcond2.8%
pump
Ip1.8%
(b) Exergy flow.
Fig. 7: Energy and Exergy flow in WHR system at optimal condition for Th,in = 100oC using R1216.
Shown in Fig. 8 are the values of mwf versus Pevap for Th,in = 100oC. Hence, lines are used to represent results for working
fluids having critical temperatures lower than Th,in and symbols are used otherwise, and same convention is followed in Figs. 8
to 10. The values of mwf increase with increase in Pevap. However, these values are widely different between the working
fluids as these depend on fluid’s liquid-phase specific heat capacity. Shown in Fig. 9 are the values of Wnet versus Tevap,sat for
Th,in = 100oC. It is seen that the net work increase with increase in Tevap,sat for all the fluids, and the maximum output works
are reasonably close.
JERT-20-1857 12 Haq
The values of three exergy based performance parameters: εcy, εht and εo for several heat source temperatures are
plotted in Fig. 10. For a given working fluid, the increase in Tevap,sat results in the increase in the evaporator pressure and the
inlet pressure of the expander while the expander outlet pressure is fixed by the condensation temperature. Hence, increase
in Tevap,sat results in the increase of the net output power of the ORC cycle because of the higher expansion ratio in the
expander and leads to higher values of εcy. It is also seen, in Fig. 10, that increase in Th,in results in higher evaporator
temperatures and with higher values of εcy. Hence, the values of εcy increase with Tevap,sat and the maximum values for all
the working fluids are found close. In the evaporator, temperature difference between the heat source and the working fluid
exists because of the sensible heating of the liquid working fluid is followed by the isothermal evaporation where working
fluid temperature deviates further from the hot source temperature. The values of εht vary significantly, and therefore affect
the overall performance of the system. Hence, effectiveness of the heat exchange process in the evaporator is affected by
the mass flow rate of the working fluid and the temperature deviation from the heat source fluid. Larger mass flow rates
and larger the temperature difference lead to increase in the exergy destruction in the evaporator [45]. Moreover, working
fluid’s thermophysical properties like specific heat capacity and the latent heat of evaporation play vital role to determine
the mass flow rate and the temperature profile of the working fluid. Although specific heat of the working fluid is not very
temperature sensitive, the latent heat of evaporation is reduced with increase in the saturation temperature. At low Tevap,sat,
the temperature of the working fluid leaving the evaporator may be superheated (as can be seen in Fig. 5) with low mass
flow rate and therefore may achieve good εht. However, with increase in Tevap,sat, values of the mass flow rate increase
with reduction in the evaporator exit temperature and with lower values of εht. However, at higher values of Tevap,sat, mass
flow rate is increased and the working fluid gets a significant amount of sensible heating where temperature curve can be
close the heat source fluid temperature and isothermal evaporation follows, and results in less deviation from heat source
temperature. Therefore, exergy destruction in the evaporator is reduced with increase in the Tevap,sat. Hence, the values of
εht initially decrease to a minimum and then increase with increase in Tevap,sat. It is observed that, one can draw a straight
line approximately indicating the values of εht once the minima is reached in the plot of εht versus Tevap,sat (Fig. 10), for all
the fluids considered and for all the heat source temperatures. Overall effectiveness of the WHR system is the result of the
combined effectiveness of the heat exchange process in the evaporator and the ORC cycle, and their values increase with
increase in Tevap,sat, and increase in Th,in also increase Tevap,sat and results in the higher values of εo at higher heat source
temperatures.
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Mass
flow
rate
,m
wf
(kg/s
)
Evaporator pressure, Pevap (MPa)
R1216
R1234yf
R227ea
R1234ze(E)
perfluorobutane
RC318
R124
R236fa
isobutane
R236ea
isobutene
butene
Fig. 8: Variation of mwf with Pevap for Th,in =100oC.
JERT-20-1857 13 Haq
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
55 56 57 58 59 60 61 62 63 64 65 66 67 68N
et
outp
ut
work
rate
,W
net
(kW
)Evaporator saturation temperature, Tevap,sat (oC)
R1216
R1234yf
R227ea
R1234ze(E)
perfluorobutane
RC318
R124
R236fa
isobutane
R236ea
isobutene
butene
Fig. 9: Variation of Wnet with Tevap,sat for Th,in = 100oC.
Key optimal operating and performance parameters obtained from the present study is summarized in Table 5. Hence,
the working fluids are arranged in the ascending order of the fluid’s critical temperatures, maximum values of the parameters
for a given source temperature are underlined and the optimal working fluids are indicated bold-faced. Following observa-
tions can also be made:
A. For a given source temperature:
- optimal working fluid’s Tcr is lower than Th,in,
- values of mwf and Pevap are unrelated to Tcr,
- values of Tevap,sat and T03 show some trend to decrease with increase in Tcr,
- no pattern/relationship is recognised between the performance parameters (εcy, εht and εo) and Tcr.
B. With increase in source temperatures:
- performance parameters (εcy, εht and εo) increase with increase in Th,in,
- values of mwf and Pevap are unrelated to Th,in,
- For Th,in ≥ 200oC, many super-dry working fluids are used and most of these exhibit higher degree of superheat
of the vapour leaving the turbine and consequent higher losses to the condenser. These fluids offer lower overall
performance with high values of εht.
- optimal working fluids are either ‘isentropic’ or ‘dry’ type.
Shown in Fig. 11 are the net work output and exergy losses versus Th,in for optimum operating conditions with optimal
working fluids. It is noted that, the optimum working fluids are either ‘isentropic’ or ‘dry’ type, although many super-dry
type working fluids are used for higher source temperatures. In Fig. 11(a), it is seen that, the supply of exergy increase
with temperature, net output work also increases with it. Figure 11(a) shows the quantitative data, and Fig. 11(b) shows the
percentage-wise results. Clearly, percentage of net output work increases and exergy destructions decrease with increase in
source temperature. Overall exergy efficiency is achieved at high source temperature.
In the present study, the correlations between heat source temperature (Th,in) and critical properties of optimal working
fluid (Tcr and Pcr), some optimum operating parameters (Tevap,sat, Pevap, Pcond and mwf) and optimum performance parameters
(εcy, εht and εo) are explored using statistical data analysis. A graphical representation of the estimated correlation coefficient,
r (also known as Pearson’s r), of the key parameters for the optimal working fluid and the optimum operating conditions
JERT-20-1857 14 Haq
56
58
60
62
64
66
68
70
72
44
46
48
50
52
28
29
30
31
32
33
34
35
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
ǫ cy
(%)
R1216
R1234yf
R227ea
R1234ze(E)
perfluorobutane
RC318
R124
R236fa
isobutane
R236ea
isobutene
butene
ǫ ht
(%)
ǫ o(%
)
Evaporator pressure, Pevap (MPa)
(a) Th,in =100oC.
45
50
55
60
65
70
75
80
50
55
60
65
70
25
30
35
40
45
50
55
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
ǫ cy
(%)
R227ea
R1224ze(E)
perflurobutane
RC318
R124
R236fa
isobutane
R236ea
isobutene
butene
butane
R245fa
R1233zd(E)
R245ca
R123
R36mfc
isopentane
ǫ ht
(%)
ǫ o(%
)
Evaporator pressure, Pevap (MPa)
(b) Th,in = 150oC.
404550556065707580
50
55
60
65
70
75
80
25
30
35
40
45
50
55
60
0.0 0.5 1.0 1.5 2.0 2.5
ǫ cy
(%)
butane
R245fa
R1233zd(E)
R245ca
R123
R36mfc
isopentane
R141b
R113
isohexane
pentante
hexane
cyclopentane
MM
ǫ ht(%
)ǫ o
(%)
Evaporator pressure, Pevap (MPa)
(c) Th,in = 200oC.
40
50
60
70
80
505560657075808590
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0 2.5
ǫ cy
(%)
R141b
R113
isohexane
pentante
hexane
cyclopentane
MM
heptane
isooctane
cyclohexane
benzene
octane
ǫ ht
(%)
ǫ o(%
)
Evaporator pressure, Pevap (MPa)
(d) Th,in = 250oC.
30
40
50
60
70
80
556065
7075808590
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
ǫ cy
(%)
heptane
isooctane
cyclohexane
benzene
octane
D4
toluene
nonane
p-xylene
m-xylene
ethylbenzene
decane
ǫ ht
(%)
ǫ o(%
)
Evaporator pressure, Pevap (MPa)
(e) Th,in = 300oC.
Fig. 10: Effects of Tevap,sat on εcy, εht and εo for Th,in = 100, 150, 200, 250 and 300oC.
JERT-20-1857 15 Haq
Table 5: Optimal operating and performance parameters.
(a) Th,in = 100oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)R1216 0.355 2.138 67.8 67.8 30 67.9 51.5 35.0R1234yf 0.28 1.786 63.8 63.8 30 68.4 49.3 33.7R227ea 0.343 1.309 64.5 64.5 31.8 69.4 49.5 34.4R1234ze(E) 0.246 1.298 60.7 60.7 30 69.2 47.3 32.7pefluorobutane 0.385 0.840 66.3 66.3 43.1 68.9 50.2 34.6RC318 0.355 0.918 63.7 63.7 35.5 70 49 34.3R124 0.279 0.985 59.5 59.5 30 69.6 46.4 32.3R236fa 0.272 0.771 60.4 60.4 30 70.1 47 32.9isobutane 0.123 0.846 58.9 58.9 30 69.6 46 32.0R236ea 0.254 0.594 59.5 59.5 30 70.3 46.4 32.6isobutene 0.114 0.739 57.7 57.7 30 69.6 45.1 31.4butene 0.114 0.715 57.4 57.4 30 69.6 44.9 31.2
(b) Th,in = 125oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)R1234yf 0.376 2.332 76.3 87.6 47.9 69.8 59.2 41.3R227ea 0.486 1.980 82.9 85.0 46.1 70.8 61.6 43.6R1234ze(E) 0.384 1.814 75.3 75.3 30.0 71.8 57.7 41.4perfluorobutane 0.550 1.398 88.7 88.7 55.2 69.2 63.1 43.6RC318 0.526 1.417 82.4 82.4 44.2 71.9 60.9 43.8R124 0.436 1.289 70.9 70.9 30.0 72.1 54.9 39.6R236fa 0.421 1.062 73.2 73.2 31.1 72.7 56.2 40.9isobutane 0.192 1.063 69.0 69.0 30.0 72.1 53.6 38.6R236ea 0.394 0.791 70.4 70.4 30.7 72.9 54.4 39.7isobutene 0.181 0.898 66.0 66.0 30.0 72.0 51.4 37.0butene 0.181 0.860 65.2 65.2 30.0 71.9 50.8 36.5butane 0.177 0.739 66.1 66.1 30.0 72.2 51.5 37.2R245fa 0.334 0.553 66.4 66.4 30.0 72.6 51.7 37.5R1233zd(E) 0.339 0.440 64.3 64.3 30.0 72.4 50.1 36.3R245ca 0.311 0.383 65.3 65.3 30.0 72.7 50.8 37.0
(c) Th,in = 150oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)R227ea 0.486 1.981 83.0 129.8 98.4 58.6 67.1 39.3R1234ze(E) 0.442 2.484 90.2 103.7 51.9 72.5 65.4 47.4perfluorobutane 0.567 1.559 93.9 123.5 95.8 57.6 68.6 39.5RC318 0.577 1.881 95.7 113.5 77.3 66.3 67.9 45.0R124 0.570 2.214 96.4 96.4 30.0 74.1 67.2 49.8R236fa 0.538 1.971 100.9 100.9 38.7 74.6 68.7 51.2isobutane 0.250 1.565 87.6 87.6 32.5 74.2 63.0 46.8R236ea 0.509 1.251 89.5 89.5 38.3 75.0 63.7 47.8isobutene 0.240 1.222 79.9 79.9 30.0 74.2 58.7 43.6butene 0.242 1.149 78.2 78.2 30.0 74.0 57.7 42.7butane 0.233 1.005 79.7 79.7 30.0 74.4 58.6 43.6R245fa 0.440 0.796 80.3 80.3 30.0 74.9 58.9 44.1R1233zd(E) 0.452 0.591 75.7 75.7 30.0 74.5 56.0 41.7R245ca 0.412 0.534 77.5 77.5 30.0 74.9 57.1 42.7R123 0.511 0.402 72.4 72.4 30.0 74.3 53.7 39.9R365mfc 0.415 0.337 78.4 78.4 35.8 75.2 57.7 43.4isopentane 0.239 0.420 76.6 76.6 32.7 74.8 56.6 42.3
(d) Th,in = 175oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)isobutane 0.275 2.568 114.3 119.3 54.5 74.5 73.1 54.4R236ea 0.566 2.306 118.6 121.4 58.1 74.8 73.8 55.2isobutene 0.285 2.147 108.5 108.5 32.3 75.8 70.5 53.5butene 0.289 1.911 103.6 103.6 30.0 75.8 68.5 51.9butane 0.275 1.674 104.8 104.8 38.1 76.1 68.9 52.5R245fa 0.521 1.424 105.4 105.4 37.8 76.7 68.9 52.8R1233zd(E) 0.546 0.917 94.2 94.2 30.4 76.4 64.0 48.9R245ca 0.493 0.863 96.8 96.8 37.7 76.8 65.1 49.9R123 0.623 0.584 87.2 87.2 30.0 76.2 60.3 45.9R365mfc 0.491 0.557 97.8 97.8 45.8 76.7 65.5 50.2isopentane 0.284 0.645 94.8 94.8 42.3 76.5 64.3 49.2R141b 0.496 0.402 78.1 78.1 30.0 75.5 54.8 41.4R113 0.686 0.308 85.8 85.8 32.8 76.4 59.4 45.4isohexane 0.282 0.243 90.7 90.7 43.0 76.6 62.1 47.6
(e) Th,in = 200oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)butane 0.286 2.665 130.7 139.6 65.8 75.2 76.7 57.6R245fa 0.546 2.464 132.5 141.1 65.0 75.9 76.7 58.3R1244zd(E) 0.633 2.278 134.0 140.7 63.4 76.0 76.5 58.1R245ca 0.546 1.735 129.3 129.3 51.2 77.6 75.0 58.1R123 0.710 0.995 110.9 110.9 35.0 77.7 68.9 53.5R365mfc 0.538 1.072 126.9 126.9 61.1 76.8 74.2 57.0isopentane 0.311 1.163 123.5 123.5 57.3 77.0 73.5 56.6R141b 0.578 0.592 94.1 94.1 30.0 77.1 61.3 47.3R113 0.779 0.500 105.9 105.9 42.5 77.8 66.7 51.9Isohexane 0.313 0.423 113.3 113.3 56.9 77.2 69.8 53.9pentane 0.305 0.834 115.8 115.8 51.5 77.5 70.8 54.9hexane 0.307 0.306 108.7 108.7 51.9 77.6 68.0 52.8cyclopentane 0.329 0.292 85.6 85.6 30.0 76.7 56.7 43.5MM 0.396 0.214 128.6 128.6 82.9 72.8 74.4 54.1
(f) Th,in = 225oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)R123 0.755 2.524 160.8 160.8 49.3 78.3 81.5 63.8R365mfc 0.551 2.180 163.8 165.4 86.7 74.6 81.9 61.1isopentane 0.316 2.356 164.1 165.0 83.5 75.0 82.6 61.9R141b 0.639 1.014 119.1 119.1 30.0 78.4 69.8 54.7R113 0.841 0.914 134.6 134.6 55.9 78.3 74.6 58.5isohexane 0.329 0.813 144.5 144.5 76.1 76.4 77.6 59.3pentane 0.318 1.782 156.5 156.5 71.4 76.9 80.6 62.0hexane 0.325 0.581 137.1 137.1 69.4 77.3 75.5 58.4cyclopentane 0.367 0.465 104.7 104.7 30.0 78.2 64.0 50.1MM 0.411 0.420 158.5 158.5 104.5 70.2 79.9 56.1heptane 0.329 0.240 130.8 130.8 68.4 77.5 73.6 57.0isooctane 0.350 0.289 141.0 141.0 85.2 74.7 76.6 57.2
(g) Th,in = 250oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)R141b 0.670 2.429 168.0 168.0 43.0 79.1 81.7 64.6R113 0.867 2.112 182.6 182.6 74.9 77.7 83.7 65.1isohexane 0.329 1.812 190.4 190.4 102.2 74.0 85.4 63.2pentane 0.316 2.335 173.0 187.4 104.8 73.2 83.3 61.0hexane 0.331 1.183 174.5 174.5 92.2 75.7 82.5 62.5cyclopentane 0.389 0.861 133.7 133.7 37.7 79.4 72.9 57.9MM 0.416 0.820 193.4 193.4 129.1 66.9 84.5 56.6heptane 0.339 0.480 162.0 162.0 89.0 76.2 79.8 60.8isooctane 0.356 0.555 173.0 173.0 108.4 72.2 82.1 59.3cyclohexane 0.385 0.390 133.3 133.3 51.0 79.5 72.6 57.8benzene 0.405 0.224 108.3 108.3 30.0 78.8 63.1 49.7octane 0.343 0.223 156.7 156.7 88.3 76.3 78.6 60.0
(h) Th,in = 275oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)pentane 0.316 2.335 173.0 215.4 137.7 68.3 83.4 57.0hexane 0.327 2.082 209.2 213.7 123.2 72.2 87.3 63.0cyclopentane 0.393 1.919 179.0 179.0 60.8 79.8 82.8 66.0MM 0.414 1.278 219.6 225.8 157.9 62.5 87.3 54.6heptane 0.341 0.965 199.1 199.1 113.6 74.0 85.1 63.0isooctane 0.354 1.059 210.0 210.0 135.1 68.9 86.8 59.8cyclohexane 0.392 0.769 167.2 167.2 72.5 79.4 79.9 63.4benzene 0.430 0.410 133.6 133.6 30.0 79.9 70.5 56.3octane 0.346 0.452 189.7 189.7 111.6 74.2 83.6 62.0D4 0.488 0.261 217.3 217.3 161.6 60.7 86.2 52.3toluene 0.434 0.194 135.1 135.1 36.0 80.0 71.0 56.8nonane 0.349 0.176 173.0 173.2 113.5 73.4 80.6 59.1
(i) Th,in = 300oC.
working mwf Pevap Tevap,sat T03 T04 εcy εht εo
fluid (kg/s) (MPa) (oC) (oC) (oC) (%) (%) (%)heptane 0.335 1.850 239.9 240.5 144.0 70.5 89.5 63.1isooctane 0.347 1.757 243.5 246.2 165.6 64.8 90.1 58.4cyclohexane 0.388 1.581 210.4 210.4 100.4 77.9 86.5 67.4benzene 0.442 0.823 167.8 167.8 40.2 80.6 78.1 63.0octane 0.344 0.898 227.6 227.6 138.1 71.5 87.8 62.7D4 0.487 0.485 249.9 249.9 187.9 57.2 88.7 50.7toluene 0.445 0.394 166.6 166.6 54.2 80.7 77.9 62.9nonane 0.349 0.176 173.0 204.4 144.6 68.2 79.9 54.5p-Xylene 0.443 0.213 168.5 168.5 64.5 80.5 78.2 63.0m-Xylene 0.443 0.199 166.1 166.1 62.8 80.5 77.7 62.6ethylbenze 0.436 0.244 172.3 172.3 69.4 80.3 79.1 63.5decane 0.351 0.106 175.9 202.0 142.6 68.7 80.3 55.2
JERT-20-1857 16 Haq
0
20
40
60
80
100
100 125 150 175 200 225 250 275 300
0
20
40
60
80
100
100 125 150 175 200 225 250 275 300
Exerg
yconsum
ption
(kW
)
Wnet
IpItIht
Ψcond
Ψh,out
R1216RC318
R236fa
R236ea
R245fa
R123
R113
cyclopentane
cyclohexane
(a)
(b)E
xerg
yconsum
ption
(%)
Heat source temperature, Th,in (oC)
(a)
(b)
Fig. 11: Work output and exergy destruction for Th,in = 100o to 300oC for optimal working fluid with optimal operating
conditions: (a) quantitative results, (b) percentage-wise results.
are displayed in the form of a heat-map in Fig. 12. Hence, the value of r is a measure of the extent to which the variables
are linearly related and the value lies between +1 and -1: a value near +1 indicates a strong positive linear relationship,
whereas a value close to -1 suggests a strong negative linear relationship, and a value close to 0 does not rule out any strong
relationship – there could still be a strong relationship but one that is not linear [46]. It is seen in Fig. 12 that the values of Tcr,
Pcr, Tevap,sat, Pcond, εcy, εht and εo have very strong correlations with Th,in, and the values of Pcond exhibit strong correlations
to the effectiveness. However, working fluid is saturated at 30oC leaving the condenser and therefore the value of Pcond is
fixed once the working fluid is selected. It may also be noted that, Pevap is not an independent parameter, once Tevap,sat is
set, its value is also fixed. Therefore, correlations are obtained for Tcr, Pcr, Tevap,sat, εcy, εht and εo as function of Th,in for the
optimal working fluid and optimum operating conditions.
Th, in Tcr Pcr Pcond Tevap Pevap mwf εcy εht εo TevapTcr
Th, inTcr
Th, inTcrPcr
PcondTevapPevapmwfεcyεhtεo
TevapTcrTh, inTcr
0.980.91 0.86-0.87 -0.82 -0.690.99 0.97 0.88 -0.860.11 -0.063 0.29 -0.11 0.160.16 0.034 0.11 -0.37 0.24 0.670.91 0.84 0.81 -0.96 0.89 0.24 0.350.95 0.89 0.82 -0.95 0.95 0.27 0.37 0.970.95 0.89 0.84 -0.95 0.95 0.27 0.36 0.98 1-0.54 -0.67 -0.42 0.39 -0.48 0.74 0.58 -0.37 -0.34 -0.360.3 0.11 0.4 -0.43 0.3 0.89 0.62 0.5 0.5 0.5 0.54
−1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 0.75 1.00correlation coefficient, r
Fig. 12: Heat-map of the key optimal parameters of WHR system for Th,in = 100oC to 300oC.
JERT-20-1857 17 Haq
Shown in Fig. 13 are the variations of the optimum Tevap,sat, Tcr and Pcr plotted as function of Th,in. Values of Tevap,sat,
Tcr and Pcr are found to increase with increase in Th,in. As can be seen in Fig. 13, linear fits represent the data well and
the estimated values of r’s are 0.992, 0.982 and 0.907 for Tevap, Tcr and Pcr, respectively. The correlations with Th,in can be
expressed as:
Tevap,sat (oC) = −4.728+0.7107 Th,in (oC) (22)
Tcr (oC) = −10.71+0.9014 Th,in (oC) (23)
Pcr (MPa) = 2.116+0.007604 Th,in (oC) (24)
50
100
150
200
250
300
100 125 150 175 200 225 250 275 3000
1
2
3
4
5
Eq. (22)Eq. (23)
Eq. (24)
Tem
pera
ture
(oC
)
Pre
ssure
(MP
a)
Heat source temperature, Th,in (oC)
Tcr
Tevap,sat
Pcr
Fig. 13: Variation of optimum Tevap,sat and critical properties of the optimal working fluid for different Th,in.
Shown in Fig. 14 are the variations of εcy, εht and εo with Th,in for optimal operating conditions with optimal working
fluid. All the effectiveness values increase with increase in Th,in. It is seen that the values of εcy are less sensitive to the
variations of Th,in, while the values of εht sharply increase with an increase in Th,in, and results in a moderate increase of the
values of εo with increase in Th,in. As can be seen in Fig. 14, linear fits describe the data well and the estimated values of r’s
are 0.907, 0.949 and 0.953 for εcy, εht and εo, respectively. The correlations with Th,in can be expressed as:
εcy (%) = 65.64+0.04893 Th,in (oC) (25)
εht (%) = 41.56+0.1623 Th,in (oC) (26)
εo (%) = 25.17+0.1551 Th,in (oC) (27)
4 Conclusions
In the present study, a simple target-temperature-line approach is proposed and used to get the optimum operating
parameters and suitable working fluids for the sub-critical ORC based WHR system. It is seen that the optimal fluids have
critical temperatures lower than the heat source temperatures and the optimal fluids are either ‘isentropic’ or ‘dry’ type
fluid. At a given heat source temperature, no other pattern is recognized indicating the relationship between optimal working
fluid’s critical properties (Tcr and Pcr), evaporator saturation temperature (Tevap,sat) and performance indicators (εcy, εht and
εo). However, some optimal parameters (Tcr, Pcr and Tevap,sat) and performance indicators (εcy, εht and εo) are found linearly
correlated with the heat source temperature, and excellent correlating equations are established. These correlations offer
guidance for the pre-selection of the working fluids and predictions of the operating/performance parameters. Hence, using
the proposed target-temperature line approach and analysis with enough suitable working fluids could lead to the optimum
utilization of waste heat.
JERT-20-1857 18 Haq
30
40
50
60
70
80
90
100
100 125 150 175 200 225 250 275 300
Eq. (27)
Eq. (26)
Eq. (25)
Effectiveness
(%)
Heat source temperature, Th,in (oC)
ǫcyǫhtǫo
Fig. 14: Effects of Th,in on εcy, εht and εo for optimum operating conditions with optimal working fluid.
Acknowledgements
The project is carried out at Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh.
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